Consider the differential equation xu′′ − (x + 1)u′ + u = 0. Suppose we know the solution to the initial value problem u(1) = 2, u′(1) = 1 is u(x) = x + 1, while the solution to the initial value problem u(1) = 1, u′(1) = 1 is u(x) = e^x−1. 

(a) What is the solution to the initial value problem u(1) = 3, u′(1) = −2? 

(b) What is the general solution to the differential equation?